%0 Journal Article
%T A permutation model for free random variables and its classical analogue
%A Florent Benaych-Georges
%A Ion Nechita
%J Mathematics
%D 2008
%I arXiv
%R 10.2140/pjm.2009.242.33
%X In this paper, we generalize a permutation model for free random variables which was first proposed by Biane in \cite{biane}. We also construct its classical probability analogue, by replacing the group of permutations with the group of subsets of a finite set endowed with the symmetric difference operation. These constructions provide new discrete approximations of the respective free and classical Wiener chaos. As a consequence, we obtain explicit examples of non random matrices which are asymptotically free or independent. The moments and the free (resp. classical) cumulants of the limiting distributions are expressed in terms of a special subset of (noncrossing) pairings. At the end of the paper we present some combinatorial applications of our results.
%U http://arxiv.org/abs/0801.4229v3